/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 f(f(0(),x),1()) -> f(g(f(x,x)),x)
 f(g(x),y) -> g(f(x,y))

Proof:
 DP Processor:
  DPs:
   f#(f(0(),x),1()) -> f#(x,x)
   f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
   f#(g(x),y) -> f#(x,y)
  TRS:
   f(f(0(),x),1()) -> f(g(f(x,x)),x)
   f(g(x),y) -> g(f(x,y))
  EDG Processor:
   DPs:
    f#(f(0(),x),1()) -> f#(x,x)
    f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
    f#(g(x),y) -> f#(x,y)
   TRS:
    f(f(0(),x),1()) -> f(g(f(x,x)),x)
    f(g(x),y) -> g(f(x,y))
   graph:
    f#(g(x),y) -> f#(x,y) -> f#(f(0(),x),1()) -> f#(x,x)
    f#(g(x),y) -> f#(x,y) -> f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
    f#(g(x),y) -> f#(x,y) -> f#(g(x),y) -> f#(x,y)
    f#(f(0(),x),1()) -> f#(g(f(x,x)),x) -> f#(g(x),y) -> f#(x,y)
    f#(f(0(),x),1()) -> f#(x,x) -> f#(g(x),y) -> f#(x,y)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     f(f(0(),x),1()) -> f(g(f(x,x)),x)
     f(g(x),y) -> g(f(x,y))
    interpretation:
     [f#](x0, x1) = -4x0 + -8x1 + 0,
     
     [g](x0) = x0,
     
     [1] = 0,
     
     [f](x0, x1) = x0 + 4x1 + 4,
     
     [0] = 5
    orientation:
     f#(f(0(),x),1()) = x + 1 >= -4x + 0 = f#(x,x)
     
     f#(f(0(),x),1()) = x + 1 >= x + 0 = f#(g(f(x,x)),x)
     
     f#(g(x),y) = -4x + -8y + 0 >= -4x + -8y + 0 = f#(x,y)
     
     f(f(0(),x),1()) = 4x + 5 >= 4x + 4 = f(g(f(x,x)),x)
     
     f(g(x),y) = x + 4y + 4 >= x + 4y + 4 = g(f(x,y))
    problem:
     DPs:
      f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
      f#(g(x),y) -> f#(x,y)
     TRS:
      f(f(0(),x),1()) -> f(g(f(x,x)),x)
      f(g(x),y) -> g(f(x,y))
    Restore Modifier:
     DPs:
      f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
      f#(g(x),y) -> f#(x,y)
     TRS:
      f(f(0(),x),1()) -> f(g(f(x,x)),x)
      f(g(x),y) -> g(f(x,y))
     Bounds Processor:
      bound: 1
      enrichment: top-dp
      automaton:
       final states: {17,7}
       transitions:
        f{#,1}(33,3) -> 17,10
        f{#,1}(48,15) -> 17,10
        f{#,1}(39,4) -> 17,10
        f{#,1}(44,10) -> 17,10
        f{#,1}(59,16) -> 17,10
        f{#,1}(54,16) -> 17,10
        f{#,1}(35,5) -> 17,10
        f{#,1}(50,13) -> 17,10
        f{#,1}(45,17) -> 17,10
        f{#,1}(56,14) -> 17,10
        f{#,1}(41,12) -> 17,10
        f{#,1}(32,1) -> 17,10
        f{#,1}(52,11) -> 17,10
        f{#,1}(47,15) -> 17,10
        f{#,1}(58,6) -> 7*
        f{#,1}(38,2) -> 17,10
        f{#,1}(43,10) -> 17,10
        f{#,1}(53,16) -> 17,10
        f{#,1}(34,3) -> 17,10
        f{#,1}(49,13) -> 17,10
        f{#,1}(40,4) -> 17,10
        f{#,1}(60,14) -> 17,10
        f{#,1}(55,14) -> 17,10
        f{#,1}(31,1) -> 17,10
        f{#,1}(36,5) -> 17,10
        f{#,1}(51,11) -> 17,10
        f{#,1}(46,17) -> 17,10
        f{#,1}(57,6) -> 7*
        f{#,1}(37,2) -> 17,10
        f{#,1}(42,12) -> 17,10
        g1(60) -> 55*
        g1(55) -> 55,56
        g1(45) -> 46*
        g1(35) -> 36*
        g1(57) -> 58*
        g1(47) -> 47,48
        g1(37) -> 38*
        g1(59) -> 59,53
        g1(49) -> 50*
        g1(39) -> 40*
        g1(51) -> 51,52
        g1(41) -> 42*
        g1(31) -> 32*
        g1(53) -> 54*
        g1(43) -> 44*
        g1(33) -> 34*
        f1(17,14) -> 60*
        f1(12,14) -> 60*
        f1(2,14) -> 60*
        f1(3,3) -> 33*
        f1(13,13) -> 49*
        f1(4,4) -> 39*
        f1(14,14) -> 55*
        f1(4,14) -> 55*
        f1(5,5) -> 35*
        f1(15,15) -> 47*
        f1(6,6) -> 57*
        f1(16,14) -> 55*
        f1(11,14) -> 55*
        f1(16,16) -> 53*
        f1(11,16) -> 59*
        f1(1,14) -> 55*
        f1(17,17) -> 45*
        f1(13,14) -> 55*
        f1(3,14) -> 55*
        f1(10,10) -> 43*
        f1(15,14) -> 55*
        f1(10,14) -> 60*
        f1(5,14) -> 60*
        f1(15,16) -> 59*
        f1(1,1) -> 31*
        f1(11,11) -> 51*
        f1(11,15) -> 47*
        f1(2,2) -> 37*
        f1(12,12) -> 41*
        f{#,0}(12,14) -> 10*
        f{#,0}(2,12) -> 10*
        f{#,0}(17,16) -> 10*
        f{#,0}(12,16) -> 10*
        f{#,0}(2,14) -> 10*
        f{#,0}(2,16) -> 10*
        f{#,0}(13,1) -> 10*
        f{#,0}(13,3) -> 10*
        f{#,0}(3,1) -> 10*
        f{#,0}(13,5) -> 10*
        f{#,0}(3,3) -> 10*
        f{#,0}(3,5) -> 10*
        f{#,0}(13,11) -> 10*
        f{#,0}(8,11) -> 7*
        f{#,0}(3,11) -> 10*
        f{#,0}(13,13) -> 10*
        f{#,0}(8,13) -> 7*
        f{#,0}(13,15) -> 10*
        f{#,0}(3,13) -> 10*
        f{#,0}(8,15) -> 7*
        f{#,0}(13,17) -> 10*
        f{#,0}(3,15) -> 10*
        f{#,0}(8,17) -> 7*
        f{#,0}(3,17) -> 10*
        f{#,0}(14,2) -> 10*
        f{#,0}(14,4) -> 10*
        f{#,0}(4,2) -> 10*
        f{#,0}(4,4) -> 10*
        f{#,0}(9,6) -> 7*
        f{#,0}(14,10) -> 10*
        f{#,0}(9,10) -> 7*
        f{#,0}(4,10) -> 10*
        f{#,0}(14,12) -> 10*
        f{#,0}(9,12) -> 7*
        f{#,0}(4,12) -> 10*
        f{#,0}(14,14) -> 10*
        f{#,0}(9,14) -> 7*
        f{#,0}(14,16) -> 10*
        f{#,0}(4,14) -> 10*
        f{#,0}(9,16) -> 7*
        f{#,0}(4,16) -> 10*
        f{#,0}(15,1) -> 10*
        f{#,0}(10,1) -> 10*
        f{#,0}(15,3) -> 10*
        f{#,0}(5,1) -> 10*
        f{#,0}(10,3) -> 10*
        f{#,0}(15,5) -> 10*
        f{#,0}(5,3) -> 10*
        f{#,0}(10,5) -> 10*
        f{#,0}(5,5) -> 10*
        f{#,0}(15,11) -> 17,10
        f{#,0}(10,11) -> 10*
        f{#,0}(15,13) -> 17,10
        f{#,0}(5,11) -> 10*
        f{#,0}(10,13) -> 10*
        f{#,0}(15,15) -> 17,10
        f{#,0}(5,13) -> 10*
        f{#,0}(10,15) -> 10*
        f{#,0}(15,17) -> 17,10
        f{#,0}(5,15) -> 10*
        f{#,0}(10,17) -> 10*
        f{#,0}(5,17) -> 10*
        f{#,0}(16,2) -> 10*
        f{#,0}(11,2) -> 10*
        f{#,0}(16,4) -> 10*
        f{#,0}(11,4) -> 10*
        f{#,0}(1,2) -> 10*
        f{#,0}(16,6) -> 7*
        f{#,0}(11,6) -> 7*
        f{#,0}(1,4) -> 10*
        f{#,0}(16,10) -> 10,17
        f{#,0}(11,10) -> 17,10
        f{#,0}(16,12) -> 10,17
        f{#,0}(11,12) -> 17,10
        f{#,0}(1,10) -> 10*
        f{#,0}(16,14) -> 10,17
        f{#,0}(11,14) -> 17,10
        f{#,0}(1,12) -> 10*
        f{#,0}(16,16) -> 10,17
        f{#,0}(11,16) -> 17,10
        f{#,0}(1,14) -> 10*
        f{#,0}(1,16) -> 10*
        f{#,0}(17,1) -> 10*
        f{#,0}(12,1) -> 10*
        f{#,0}(17,3) -> 10*
        f{#,0}(12,3) -> 10*
        f{#,0}(2,1) -> 10*
        f{#,0}(17,5) -> 10*
        f{#,0}(12,5) -> 10*
        f{#,0}(2,3) -> 10*
        f{#,0}(2,5) -> 10*
        f{#,0}(17,11) -> 10*
        f{#,0}(12,11) -> 10*
        f{#,0}(17,13) -> 10*
        f{#,0}(12,13) -> 10*
        f{#,0}(2,11) -> 10*
        f{#,0}(17,15) -> 10*
        f{#,0}(12,15) -> 10*
        f{#,0}(2,13) -> 10*
        f{#,0}(17,17) -> 10*
        f{#,0}(12,17) -> 10*
        f{#,0}(2,15) -> 10*
        f{#,0}(2,17) -> 10*
        f{#,0}(13,2) -> 10*
        f{#,0}(13,4) -> 10*
        f{#,0}(3,2) -> 10*
        f{#,0}(3,4) -> 10*
        f{#,0}(8,6) -> 7*
        f{#,0}(13,10) -> 10*
        f{#,0}(8,10) -> 7*
        f{#,0}(3,10) -> 10*
        f{#,0}(13,12) -> 10*
        f{#,0}(8,12) -> 7*
        f{#,0}(3,12) -> 10*
        f{#,0}(13,14) -> 10*
        f{#,0}(8,14) -> 7*
        f{#,0}(13,16) -> 10*
        f{#,0}(3,14) -> 10*
        f{#,0}(8,16) -> 7*
        f{#,0}(3,16) -> 10*
        f{#,0}(14,1) -> 10*
        f{#,0}(14,3) -> 10*
        f{#,0}(4,1) -> 10*
        f{#,0}(14,5) -> 10*
        f{#,0}(4,3) -> 10*
        f{#,0}(4,5) -> 10*
        f{#,0}(14,11) -> 10*
        f{#,0}(9,11) -> 7*
        f{#,0}(4,11) -> 10*
        f{#,0}(14,13) -> 10*
        f{#,0}(9,13) -> 7*
        f{#,0}(14,15) -> 10*
        f{#,0}(4,13) -> 10*
        f{#,0}(9,15) -> 7*
        f{#,0}(14,17) -> 10*
        f{#,0}(4,15) -> 10*
        f{#,0}(9,17) -> 7*
        f{#,0}(4,17) -> 10*
        f{#,0}(15,2) -> 10*
        f{#,0}(10,2) -> 10*
        f{#,0}(15,4) -> 10*
        f{#,0}(5,2) -> 10*
        f{#,0}(10,4) -> 10*
        f{#,0}(15,6) -> 7*
        f{#,0}(5,4) -> 10*
        f{#,0}(15,10) -> 17,10
        f{#,0}(10,10) -> 10*
        f{#,0}(15,12) -> 17,10
        f{#,0}(5,10) -> 10*
        f{#,0}(10,12) -> 10*
        f{#,0}(15,14) -> 17,10
        f{#,0}(5,12) -> 10*
        f{#,0}(10,14) -> 10*
        f{#,0}(15,16) -> 17,10
        f{#,0}(5,14) -> 10*
        f{#,0}(10,16) -> 10*
        f{#,0}(5,16) -> 10*
        f{#,0}(16,1) -> 10*
        f{#,0}(11,1) -> 10*
        f{#,0}(16,3) -> 10*
        f{#,0}(11,3) -> 10*
        f{#,0}(1,1) -> 10*
        f{#,0}(16,5) -> 10*
        f{#,0}(11,5) -> 10*
        f{#,0}(1,3) -> 10*
        f{#,0}(1,5) -> 10*
        f{#,0}(16,11) -> 10,17
        f{#,0}(11,11) -> 17,10
        f{#,0}(16,13) -> 10,17
        f{#,0}(11,13) -> 17,10
        f{#,0}(1,11) -> 10*
        f{#,0}(16,15) -> 10,17
        f{#,0}(11,15) -> 17,10
        f{#,0}(1,13) -> 10*
        f{#,0}(16,17) -> 10,17
        f{#,0}(11,17) -> 17,10
        f{#,0}(1,15) -> 10*
        f{#,0}(1,17) -> 10*
        f{#,0}(17,2) -> 10*
        f{#,0}(12,2) -> 10*
        f{#,0}(17,4) -> 10*
        f{#,0}(12,4) -> 10*
        f{#,0}(2,2) -> 10*
        f{#,0}(2,4) -> 10*
        f{#,0}(17,10) -> 10*
        f{#,0}(12,10) -> 10*
        f{#,0}(17,12) -> 10*
        f{#,0}(12,12) -> 10*
        f{#,0}(2,10) -> 10*
        f{#,0}(17,14) -> 10*
        f0(12,14) -> 15*
        f0(2,12) -> 11*
        f0(17,16) -> 15*
        f0(12,16) -> 15*
        f0(2,14) -> 11*
        f0(2,16) -> 11*
        f0(13,1) -> 11*
        f0(13,3) -> 11*
        f0(3,1) -> 11*
        f0(13,5) -> 11*
        f0(3,3) -> 11*
        f0(3,5) -> 11*
        f0(13,11) -> 15*
        f0(3,11) -> 11*
        f0(13,13) -> 15*
        f0(13,15) -> 15*
        f0(3,13) -> 11*
        f0(13,17) -> 15*
        f0(3,15) -> 11*
        f0(3,17) -> 11*
        f0(14,2) -> 15,11
        f0(14,4) -> 15,11
        f0(4,2) -> 11*
        f0(14,6) -> 8*
        f0(4,4) -> 11*
        f0(4,6) -> 8*
        f0(14,10) -> 15*
        f0(4,10) -> 11*
        f0(14,12) -> 15*
        f0(4,12) -> 11*
        f0(14,14) -> 15*
        f0(14,16) -> 15*
        f0(4,14) -> 11*
        f0(4,16) -> 11*
        f0(15,1) -> 11*
        f0(10,1) -> 11*
        f0(15,3) -> 11*
        f0(5,1) -> 11*
        f0(10,3) -> 11*
        f0(15,5) -> 11*
        f0(5,3) -> 11*
        f0(10,5) -> 11*
        f0(5,5) -> 11*
        f0(15,11) -> 15*
        f0(10,11) -> 15*
        f0(15,13) -> 15*
        f0(5,11) -> 11*
        f0(10,13) -> 15*
        f0(15,15) -> 15*
        f0(5,13) -> 11*
        f0(10,15) -> 15*
        f0(15,17) -> 15*
        f0(5,15) -> 11*
        f0(10,17) -> 15*
        f0(5,17) -> 11*
        f0(16,2) -> 11*
        f0(11,2) -> 11*
        f0(16,4) -> 11*
        f0(11,4) -> 11*
        f0(1,2) -> 11*
        f0(16,6) -> 8*
        f0(11,6) -> 8*
        f0(1,4) -> 11*
        f0(6,6) -> 8*
        f0(1,6) -> 8*
        f0(16,10) -> 15*
        f0(11,10) -> 15*
        f0(16,12) -> 15*
        f0(6,10) -> 8*
        f0(11,12) -> 15*
        f0(1,10) -> 11*
        f0(16,14) -> 15*
        f0(6,12) -> 8*
        f0(11,14) -> 15*
        f0(1,12) -> 11*
        f0(16,16) -> 15*
        f0(6,14) -> 8*
        f0(11,16) -> 15*
        f0(1,14) -> 11*
        f0(6,16) -> 8*
        f0(1,16) -> 11*
        f0(17,1) -> 11*
        f0(12,1) -> 11*
        f0(17,3) -> 11*
        f0(12,3) -> 11*
        f0(2,1) -> 11*
        f0(17,5) -> 11*
        f0(12,5) -> 11*
        f0(2,3) -> 11*
        f0(2,5) -> 11*
        f0(17,11) -> 15*
        f0(12,11) -> 15*
        f0(17,13) -> 15*
        f0(12,13) -> 15*
        f0(2,11) -> 11*
        f0(17,15) -> 15*
        f0(12,15) -> 15*
        f0(2,13) -> 11*
        f0(17,17) -> 15*
        f0(12,17) -> 15*
        f0(2,15) -> 11*
        f0(2,17) -> 11*
        f0(13,2) -> 11*
        f0(13,4) -> 11*
        f0(3,2) -> 11*
        f0(13,6) -> 8*
        f0(3,4) -> 11*
        f0(3,6) -> 8*
        f0(13,10) -> 15*
        f0(3,10) -> 11*
        f0(13,12) -> 15*
        f0(3,12) -> 11*
        f0(13,14) -> 15*
        f0(13,16) -> 15*
        f0(3,14) -> 11*
        f0(3,16) -> 11*
        f0(14,1) -> 15,11
        f0(14,3) -> 15,11
        f0(4,1) -> 11*
        f0(14,5) -> 15,11
        f0(4,3) -> 11*
        f0(4,5) -> 11*
        f0(14,11) -> 15*
        f0(4,11) -> 11*
        f0(14,13) -> 15*
        f0(14,15) -> 15*
        f0(4,13) -> 11*
        f0(14,17) -> 15*
        f0(4,15) -> 11*
        f0(4,17) -> 11*
        f0(15,2) -> 11*
        f0(10,2) -> 11*
        f0(15,4) -> 11*
        f0(5,2) -> 11*
        f0(10,4) -> 11*
        f0(15,6) -> 8*
        f0(5,4) -> 11*
        f0(10,6) -> 8*
        f0(5,6) -> 8*
        f0(15,10) -> 15*
        f0(10,10) -> 15*
        f0(15,12) -> 15*
        f0(5,10) -> 11*
        f0(10,12) -> 15*
        f0(15,14) -> 15*
        f0(5,12) -> 11*
        f0(10,14) -> 15*
        f0(15,16) -> 15*
        f0(5,14) -> 11*
        f0(10,16) -> 15*
        f0(5,16) -> 11*
        f0(16,1) -> 11*
        f0(11,1) -> 11*
        f0(16,3) -> 11*
        f0(11,3) -> 11*
        f0(1,1) -> 11*
        f0(16,5) -> 11*
        f0(11,5) -> 11*
        f0(1,3) -> 11*
        f0(1,5) -> 11*
        f0(16,11) -> 15*
        f0(11,11) -> 15*
        f0(16,13) -> 15*
        f0(6,11) -> 8*
        f0(1,11) -> 11*
        f0(11,13) -> 15*
        f0(16,15) -> 15*
        f0(6,13) -> 8*
        f0(11,15) -> 15*
        f0(1,13) -> 11*
        f0(16,17) -> 15*
        f0(6,15) -> 8*
        f0(11,17) -> 15*
        f0(1,15) -> 11*
        f0(6,17) -> 8*
        f0(1,17) -> 11*
        f0(17,2) -> 11*
        f0(12,2) -> 11*
        f0(17,4) -> 11*
        f0(12,4) -> 11*
        f0(2,2) -> 11*
        f0(17,6) -> 8*
        f0(12,6) -> 8*
        f0(2,4) -> 11*
        f0(2,6) -> 8*
        f0(17,10) -> 15*
        f0(12,10) -> 15*
        f0(17,12) -> 15*
        f0(12,12) -> 15*
        f0(2,10) -> 11*
        f0(17,14) -> 15*
        00() -> 12*
        10() -> 13*
        g0(15) -> 15,16
        g0(10) -> 14*
        g0(5) -> 14*
        g0(17) -> 14*
        g0(12) -> 14*
        g0(2) -> 14*
        g0(14) -> 14*
        g0(4) -> 14*
        g0(16) -> 14*
        g0(11) -> 15,11,14
        g0(1) -> 14*
        g0(13) -> 14*
        g0(8) -> 8,9
        g0(3) -> 14*
      problem:
       DPs:
        f#(g(x),y) -> f#(x,y)
       TRS:
        f(f(0(),x),1()) -> f(g(f(x,x)),x)
        f(g(x),y) -> g(f(x,y))
      Size-Change Termination Processor:
       DPs:
        
       TRS:
        f(f(0(),x),1()) -> f(g(f(x,x)),x)
        f(g(x),y) -> g(f(x,y))
       The DP: f#(g(x),y) -> f#(x,y) has the edges:
         0 >   0
         1 >=  1
       Qed